Question

A project requires a round, concrete patio on the back of a house with a diameter of 24′. How much concrete would be required to pour the patio 6″ thick? Express your answer in cubic yards.

Answer 1

8.38 yd³

Explanation:

Use volume of a cylinder formula:
`\pi r^2h`

where r is the radius and h is the height.

Radius = half of diameter = 24 ÷ 2 = 12 ft

Height = 6 in

We need to express the answer in yards, so first convert radius and height to yards:

1 yard = 3 ft = 36 in

⇒ Radius = 12 ft = 4 yards

⇒ Height = 6 in = 1/6 yards

Substituting these values into the volume of a cylinder formula:

`\pi r^2h` =
`\pi` x 4² x 1/6

=
`(8)/(3) \pi`

= 8.38 yd³ (nearest hundredth)